The Director of a State Agency Believes That the Average

The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750. Assuming the population standard deviation is known to be $2,500 and the significance level for the test is to be 0.05, what is the critical value (stated in dollars) ?

A) For alpha = .05 and a one tailed, lower tail test, the critical value is z = -1.645. Solving for the critical x- bar: -1.645 = (x-bar - 30,000) /250, x-bar = $29,588.75
B) For alpha = .05 and a one tailed, lower tail test, the critical value is z = -1.96. Solving for the critical x- bar: -1.96 = (x-bar - 30,000) /250, x-bar = $34,211.14
C) For alpha = .05 and a one tailed, lower tail test, the critical value is z = -1.645. Solving for the critical x- bar: -1.645 = (x-bar - 30,000) /250, x-bar = $34,211.14
D) For alpha = .05 and a one tailed, lower tail test, the critical value is z = -1.96. Solving for the critical x- bar: -1.96 = (x-bar - 30,000) /250, x-bar = $30,411.25